From what I understand, the loss of the Torah portion of Keter Aram Soba (the Aleppo Codex) in 1948 is heavily lamented because it was the oldest preserved and probably most accurate text of Torah.

Although the loss of the original is a tragedy, was the text preserved through sifre torah written later, copied off of the original? Were the sifre Torah (and printed Humashim) of Halab based off the Aleppo Codex, and if yes, don't we have any? Did nobody copy it since Rambam?

IIRC, Rambam considered it authoritative and modern Yeminite Torah scrolls follow it's text, as did most sifre Torah in the Middle East at that time. However over the course of a few hundred years the text currently used by most Jews became the dominate one. If I can find where I read about this I'll change this comment to an answer. The differences are minor though IIRC, just a different number of yuds and vav's in some words.
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Robert S. BarnesOct 5 '14 at 18:22

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Apparently, at least in the last couple of centuries, the Keter was jealously guarded and people indeed were not permitted to make copies of it. (There may well have been other copies of it from Rambam's times or the next couple of centuries after that, but if so, they either haven't survived or are unknown.)

One important source that we do have - R. Mordechai Breuer used it, I believe, in the preparation of his "Keter Yerushalayim" referenced in Reb Chaim HaQoton's answer - is a list of questions that R. Yaakov Saphir, a 19th-century traveler and talmid chacham, sent to Aleppo, with their replies on what is written in the Keter. This has been published from manuscript, although according to the introduction there it's not his original autograph and so may not be 100% accurate.

Since they are not annotated in any way, it's impossible to know of any given sefer tora what it's model was. Further, even if we knew that a given sefer was exactly copied from the Keter (Aleppo Codex), that would not help us recreate the vowels or accents. However, by taking the majority reading of specific selected Masoretic manuscripts, Rabbi Breuer was able to determine the reading of the Keter with extremely high accuracy.